First slide

Binomial theorem for positive integral Index

Question

If the coefficients of $(2 r + 4)$ th and $(r - 2)$ th terms in the expansion of ${(1 + x)}^{18}$ are equal, then value of $r$ is

Moderate

A

5
B

6
C

7
D

9

Solution

$\begin{array}{l} ^{18} C_{2 r + 3} =^{18} C_{r - 3} \\ \Rightarrow 2 r + 3 = r - 3 or 18 = (2 r + 3) + (r - 3) \\ \Rightarrow r = - 6 or r = 6 \end{array}$

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